A Linear Programming Problem is as follows: Maximize/Minimize obj… - Vidyadip

MCQ

A Linear Programming Problem is as follows:
Maximize/Minimize objective function $Z = 2x - y +5$
Subject to the constraints
$3 x+4 y \leq 60$
$x+3 y \leq 30$
$x \leq 0, y \geq 0$
In the corner points of the feasible region are $A(0, 10), B(12, 6), C(20, 0)$ and $O(0,0),$ then which of the following is true?

✓
Minimum value of $Z$ is $-5$
B
At two corner points, value of $Z$ are equal
C
Maximum value of $Z$ is $40$
D
Difference of maximum and minimum values of $Z$ is $35$

✓

Answer

Correct option: A.

Minimum value of $Z$ is $-5$

Corner Points	Value of $Z = 2x - y + 5$
$A(0, 10)$	$Z=2(0)-10+5 = -5 ($ Minimum$)$
$B(12, 6)$	$Z2(12)-6+ 5 = 23$
$C(20, 0)$	$Z=2(20)-0+5 = 45 ($Maximum$)$
$O(0,0)$	$Z=0(0)-0+5=5$

So the minimum value of $Z$ is $-5.$

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